Discrete uninterrupted averaging in Taylor ergodic theorem
Victor V. Nosov, Vladimir P. Lukin, Evgeny V. Nosov, Andrei V. Torgaev · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2006
Aspects of construction of random functions statistical performances for discrete-uninterrupted averaging have been investigated. At the averaging, which is usually realized in practice, every discrete sequence of random function empiric values is partially averaged by a certain interval of argument variation. The evaluations of dispersion convergence rate for deviation of time average from assembly average providing convergence in probability have been obtained. It is shown that evaluations of dispersion convergence rate depend on the integral scales of random function correlation. These scales are determined by a type of averaging. They differ for uninterrupted, discrete and discrete-uninterrupted averaging. Connections between them are established. Results of reconstruction of arbitrary correlation function parameters from the equation, which binds correlation functions of direct and partial averaged random processes, are listed. It is determined that a non-averaged process correlation function may be restored satisfactorily from partially averaged data, even at large intervals of partial averaging.